# The Physics of Non–Equilibrium Reliability Phenomena

### Chapter 6 Conclusions & Outlook

#### 6.1 Conclusions

The present work addressed open questions associated with non–equilibrium reliability issues such as the creation of defects at the Si/SiO$$_2$$ interface and the charging kinetics of pre–existing oxide traps. A profound understanding of the involved processes is not only a vital component for the description of the individual degradation regimes, hot–carrier degradation (HCD) and non–equilibrium bias temperature instability (BTI), but also an essential step towards full {$$V_\mathrm {G},V_\mathrm {D}$$} bias space characterizations.

A major part of this thesis focuses on the interaction of energetic carriers with Si–H bonds at the Si/SiO$$_2$$ interface region. New concepts and methodologies have been introduced to capture the intricate behaviour of hot–carrier induced degradation. A resonance scattering excitation mechanism has been identified as the main driving force of Si–H bond rupture and the subsequent creation of an interface defect. While this idea was already proposed in one of the pioneering papers published by the group of Hess, it was not rigorously pursued in any implementation. Ultimately, the derived framework considers all relevant external influences such as energetic carriers and an applied electric field as well as dissipation processes due to the surrounding environment. In conjunction with ab initio methods which allowed to extract essential parameters for all individual contributions, the presented modeling approach provides detailed insight into the phenomenon of HCD. Additionally, density functional theory calculations have been used to finally reveal the microscopic Si–H bond breaking mechanism at the semiconductor–oxide interface. Subsequent H migration trajectories and passivation reactions based on H$$_2$$ cracking have been further investigated to establish a complete picture of hydrogen at the Si/SiO$$_2$$ interface. The established model has been applied to capture the trends of HCD in two devices, an nMOSFET and a pMOSFET with different channel lengths. Together with a detailed analysis the simulation results give new insight into the degradation characteristics and provide an accurate description on a microscopic level using a consistent parameter set.

The physically meaningful concept of a resonance based mechanism, furthermore, highlights some intriguing findings. First, the approach is virtually free of any fitting parameters due to its combination with ab initio based methods. Second, the previously used phenomenological multiple carrier and single carrier processes are actually a manifestation of the same fundamental interaction, a resonance scattering excitation. Moreover, besides the physical interpretation, the presented formulation allows for another intuitive understanding of another peculiarity of HCD: Occasional reports suggest that the degradation in nMOS devices is larger than in their pMOS counterpart. Considering that the available resonance state for holes is higher in energy than for electrons, as suggested by the DFT study, would facilitate the first physically reasonable explanations. Finally, note, that the methodology is free of empirical parameters and widely applied in the field of quantum chemistry describing surface phenomena. Thus, the formulations is generally applicable to new and emerging material combinations, such as SiGe or graphene based devices.

The second topic discussed in this thesis the dynamics of oxide defects interacting with energetic carriers. Usually, charge trapping at pre–existing defect sites in SiO$$_2$$ is investigated around the respective worst case conditions for BTI, namely at equilibrium conditions. Unfortunately, only a very limited number of studies is available reporting data regarding the behaviour of oxide defects with increasing drain bias stress. However, the vast majority of these observations concludes that a simple electrostatic consideration is not sufficient to explain the measurements. Therefore, the current 4–state NMP framework has been extended towards non–equilibrium energy distribution functions (EDFs), which includes the interaction with a heated carrier ensemble in the valence and conduction band1 Since the NMP model already takes a whole band of states into account using the concept of the lineshape function (LSF), the natural extension only requires the implementation of the respective EDFs. Two model variants with increasing complexity have been introduced: a full non–equilibrium variant NMP$$_\mathrm {neq.}$$, which considers a self–consistent solution of the coupled Boltzmann transport equation for electrons and holes, as well as an extended approach NMP$$_\mathrm {eq.+II}$$ where the effect of impact ionization (II) has been approximated using semi–empirical models.

The different model variants have been compared against experimentally recorded characteristics for two individual oxide defects for a broad range of stress conditions. The rather puzzling measurements trends can be fully understood by taking the interactions with energetic minority and secondary carriers into account. As was shown in a detailed analysis such an interplay can lead to a substantially different trap behaviour. Interestingly, the presented study reveals that even defects located at the source side of the device can be heavily affected by an applied drain bias.

Finally, both individual modeling frameworks have been used in conjunction culminating in a rigorous simulation study of a pMOSFETs full {$$V_\mathrm {G},V_\mathrm {D}$$} bias map. The comprehensive study reveals the degradation and recovery dynamics over a wide range of bias conditions by explicitly modeling the charge transition kinetics of oxide defects as well as the creation of interface states. The simulation results properly capture the experimental trends and are further supported by a detailed analysis of the involved mechanisms. Additionally a dedicated experiment performing alternating BTI and HCD stress cycles revealed a peculiar feature of accelerated recovery conditions.

The established results provide an in–depth description and understanding of degradation and recovery dynamics in full bias space and ultimately stress the conceptual limits of independent degradation regimes.

1 This, however, depends on the applied bias conditions.